Related papers: Computing the Skorokhod Distance between Polygonal…
We propose a procedure for estimating the Schr\"odinger bridge between two probability distributions. Unlike existing approaches, our method does not require iteratively simulating forward and backward diffusions or training neural networks…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
The Dynamic Time Warping (DTW) distance is a popular measure of similarity for a variety of sequence data. For comparing polygonal curves $\pi, \sigma$ in $\mathbb{R}^d$, it provides a robust, outlier-insensitive alternative to the…
The Frechet distance is a well-studied and very popular measure of similarity of two curves. Many variants and extensions have been studied since Alt and Godau introduced this measure to computational geometry in 1991. Their original…
The minimum orbital intersection distance is used as a measure to assess potential close approaches and collision risks between astronomical objects. Methods to calculate this quantity have been proposed in several previous publications.…
We investigate the modified trace distance measure of coherence recently introduced in [Phys. Rev. A 94, 060302(R) (2016)]. We show that for any single-qubit state, the modified trace norm of coherence is equal to the $l_{1}$-norm of…
We demonstrate relationships between the classic Euclidean algorithm and many other fields of study, particularly in the context of music and distance geometry. Specifically, we show how the structure of the Euclidean algorithm defines a…
We revisit the problem of certifying the correctness of approximate solution paths computed by numerical homotopy continuation methods. We propose a conceptually simple approach based on a parametric variant of the Krawczyk method from…
This paper studies the properties of a new lower bound for the natural pseudo-distance. The natural pseudo-distance is a dissimilarity measure between shapes, where a shape is viewed as a topological space endowed with a real-valued…
We survey some basic results on the Gromov-Prohorov distance between metric measure spaces. (We do not claim any new results.) We give several different definitions and show the equivalence of them. We also show that convergence in the…
This work introduces a notion of approximate probabilistic trace equivalence for labelled Markov chains, and relates this new concept to the known notion of approximate probabilistic bisimulation. In particular this work shows that the…
Imitation learning algorithms have been interpreted as variants of divergence minimization problems. The ability to compare occupancy measures between experts and learners is crucial in their effectiveness in learning from demonstrations.…
In this paper, we study the problem of map matching with travel time constraints. Given a sequence of $k$ spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by…
The Persistent Homology Transform (PHT) summarizes a shape in $\mathbb{R}^m$ by collecting persistence diagrams obtained from linear height filtrations in all directions on $\mathbb{S}^{m-1}$. It enjoys strong theoretical guarantees,…
Modern tracking technology has made the collection of large numbers of densely sampled trajectories of moving objects widely available. We consider a fundamental problem encountered when analysing such data: Given $n$ polygonal curves $S$…
Scarf's algorithm--a pivoting procedure that finds a dominating extreme point in a down-monotone polytope--can be used to show the existence of a fractional stable matching in hypergraphs. The problem of finding a fractional stable matching…
We extend our previous algorithm computing the minimum orbital intersection distance (MOID) to include hyperbolic orbits, and mixed combinations ellipse--hyperbola. The MOID is computed by finding all stationary points of the distance…
Modern time series analysis requires the ability to handle datasets that are inherently high-dimensional; examples include applications in climatology, where measurements from numerous sensors must be taken into account, or inventory…
We introduce in this paper a novel strategy for efficiently approximating the Sinkhorn distance between two discrete measures. After identifying neglectable components of the dual solution of the regularized Sinkhorn problem, we propose to…
This short note introduces the harmonic indel distance (HID), a new distance between strings where the cost of an insertion or deletion is inversely proportional to the string length. We present a closed-form formula and show that the HID…